I've been thinking about the following set-up involving three parties, Alice, Bob and Charlie:
- Bob and Charlie decide among themselves who is going to receive a bit from Alice (perhaps by a coin toss)
- Some protocol is then executed in which Alice transfers a bit to the decided on person.
The protocol is defined as secure if:
- Alice cannot change her bit based on which of Bob or Charlie it is that receives the bit (the transfer is "party independent")
- Supposing Bob was decided on to receive the bit, Charlie cannot learn the value of the bit handed over by Alice, and vice versa.
My question is this: is there a studied task which is similar to what is described above? Or is this perhaps secretly equivalent to some apparently distinct task? (it sounds a bit like some form of oblivious transfer)